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Behavioural equivalence for infinite systems — Partially decidable!

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Book cover Application and Theory of Petri Nets 1996 (ICATPN 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1091))

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Abstract

For finite-state systems non-interleaving equivalences are computationally at least as hard as interleaving equivalences. In this paper we show that when moving to infinite-state systems, this situation may change dramatically.

We compare standard language equivalence for process description languages with two generalizations based on traditional approaches capturing non-interleaving behaviour, pomsets representing global causal dependency, and locality representing spatial distribution of events.

We first study equivalences on Basic Parallel Processes, BPP, a process calculus equivalent to communication free Petri nets. For this simple process language our two notions of non-interleaving equivalences agree. More interestingly, we show that they are decidable, contrasting a result of Hirshfeld that standard interleaving language equivalence is undecidable. Our result is inspired by a recent result of Esparza and Kiehn, showing the same phenomenon in the setting of model checking.

We follow up investigating to which extent the result extends to larger subsets of CCS and TCSP. We discover a significant difference between our non-interleaving equivalences. We show that for a certain non-trivial subclass of processes between BPP and TCSP, not only are the two equivalences different, but one (locality) is decidable whereas the other (pomsets) is not. The decidability result for locality is proved by a reduction to the reachability problem for Petri nets.

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Authors and Affiliations

  1. Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000, Aarhus C.

    Kim Sunesen & Mogens Nielsen

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  1. Kim Sunesen
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  2. Mogens Nielsen
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Jonathan Billington Wolfgang Reisig

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© 1996 Springer-Verlag Berlin Heidelberg

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Sunesen, K., Nielsen, M. (1996). Behavioural equivalence for infinite systems — Partially decidable!. In: Billington, J., Reisig, W. (eds) Application and Theory of Petri Nets 1996. ICATPN 1996. Lecture Notes in Computer Science, vol 1091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61363-3_25

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  • DOI: https://doi.org/10.1007/3-540-61363-3_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61363-3

  • Online ISBN: 978-3-540-68505-0

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